Necessary and sufficient local convergence condition of one class of iterative aggregation–disaggregation methods

This paper concludes one part of the local convergence analysis of a certain class of iterative aggregation–disaggregation methods for computing a stationary probability distribution vector of an irreducible stochastic matrix B. We show that the local convergence of the algorithm is determined only by the sparsity pattern of the matrix and by the choice of the aggregation groups. We introduce the asymptotic convergence rates of the normalized components of approximations corresponding to particular aggregation groups and we also specify an upper bound on the rates. Copyright © 2008 John Wiley & Sons, Ltd.